Oh gosh, @gnandanpai, I see that I didn't respond to your question. Apologies.
You pose a valid question. If you don't know what department to start with, how do you apply. Luckily, Mayo Clinic will help guide you through the process. @artscaping can tell you about her experience using the online form. The form has 4 section and the first one asks about your main concern. You do not have to designate which department you'd like to be seen by.
If your request just doesn't fit into the boxes of the form well or you don't like forms, feel free to call Mayo Clinic at the location of your choice (AZ, FL or MN). The schedulers will walk you through the process.